Abstract
Since Konolige's translation of default logic into strongly grounded autoepistemic logic, several other variants of Moore's original autoepistemic logic that embody default logic have been studied. All these logics differ significantly from Moore's autoepistemic logic (standard AEL) in that expansions are subject to additional groundedness-conditions. Hence, the question naturally arises whether default logic can be translated into standard AEL at all. We show, that a modular translation is not possible. However, we exhibit a a faithful polynomial-time translation from propositional default logic into standard AEL which is nonmodular. It follows that the expressive power of standard AEL is strictly greater than that of default logic. Our translation uses as important intermediate step an embedding of Marek's and Truszczyński's nonmonotonic logic N into standard AEL.
This paper also appears in the proceedings of the 13th International Joint Conference on Artificial Intelligence IJCAI-93, August 27 – September 03, 1993,Chambery, France. This is a short version of the full paper [4] available from the author by email/ftp.
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References
J. Delgrande and W. Jackson. Default Logic Revisited. In Proc. KR-91
Th. Eiter and G. Gottlob Reasoning with Parsimonious and Moderately Grounded Expansions. Fundamenta Informaticae, 17:31–53, 1992.
M.C. Fitting, W. Marek, and M. Truszczyński. The Pure Logic of Necessitation. The Journal of Logic and Computation, 2(3):349–373, 1992.
G. Gottlob. The Power of Beliefe: Translating Default Logic Into Standard Autoepistemic Logic (Extended Report). Report CD-TR-92/34, TU Wien, Paniglgasse 16, A-1040 Wien, Austria, 1992.
G. Gottlob. Complexity Results for Nonmonotonic Logics. The Journal of Logic and Computation, 2:3:397–425, June 1992.
T. Imielinski. Results on Translating Defaults to Circumscription. In Proc. IJCAI-1985, 1985.
M. Kaminski. Embedding a Default System into Nonmonotonic Logic. Fundamenta Informaticae, 14:345–354, 1991.
K. Konolige. On the Relationship between Default and Autoepistemic Logic. AIJ, 35:343–382, 1988. (+ Errata, vol 41(1989/90), p.115, 1989).
F. Lin and Y. Shoham. Epistemic Semantics for Fixed-Point Non-Monotonic Logics. In Proc. TARK-90, pp. 111–120. 1990.
W. Marek, G.F. Schwartz, and M. Truszczynski. Modal Nonmonotonic Logics: Ranges, Characterization, Computation. Proc. KR-91.
W. Marek and M. Truszczynski. Relating Autoepistemic and Default Logics. In Proc. KR-89.
W. Marek and M. Truszczyński. Modal logic for default reasoning. Annals of Mathematics and Artificial Intelligence, 1:275–302, 1990.
D. McDermott. Non-Monotonic Logic II: Nonmonotonic Modal Theories. JACM, 29:33–57, 1982.
R.C. Moore. Semantical Considerations on Nonmonotonic Logic. AIJ, 25:75–94, 1985.
I. Niemelä. Constructive Tightly Grounded Autoepistemic Reasoning. In Proc. IJCAI-1991, 1991.
R. Reiter. A Logic for Default Reasoning. AIJ, 13:81–132, 1980.
G. Shvarts. Autoepistemic Modal Logics. In Proc. TARK-90, pp. 97–109. 1990.
P. Siegel. A Modal Language for Nonmonotonic Logic. In Proc. Workshop DRUM-S/'CEE, Marseille, France, 1990, 1990.
M. Truszczynski. Modal Interpretations of Default Logic. In Proc. IJCAI-1991, 1991.
M. Truszczynski. Embedding Default Logic into Modal Nonmonotonic Logics. Proc. Workshop on Nonmon. Reas. and LP, Washington, July 1991.
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© 1994 Springer-Verlag Berlin Heidelberg
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Gottlob, G. (1994). The power of beliefs or translating default logic into standard autoepistemic logic. In: Lakemeyer, G., Nebel, B. (eds) Foundations of Knowledge Representation and Reasoning. Lecture Notes in Computer Science, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58107-3_8
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DOI: https://doi.org/10.1007/3-540-58107-3_8
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